Question

Graph the inequality on the axes below.
y, is greater than, minus, start fraction, 5, divided by, 6, end fraction, x, minus, 5
y>−5/6x−5 on a graph with two points using slope and y intercept

Answer 1

Step 1 — y‑intercept: set x = 0 → y = −5. Plot point (0, −5).

Step 2 — use the slope −5/6: from (0, −5) go right 6 and down 5 to get the second point (6, −10). (Or go left 6 and up 5 to get (−6, 0).)

Step 3 — draw a dashed line through those two points (inequality is strict, ">" → do not include the line).

Step 4 — decide which side to shade. Test the origin (0,0): 0 > −5 is true, so shade the region above the line (the side containing (0,0)).

Summary of points to plot: (0, −5) and (6, −10) (or (−6, 0)). Draw a dashed line through them and shade the half‑plane above.